Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

The frequency of vibration $f$ of a mass m suspended from a spring of spring constant k is given by a relation of the type $f = c m^{x} k^{y},$ where c is a dimensionless constant. The values of $x$ and $y$ are

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Answer:

Solution:

$f = c m^{x} k^{y};$

Spring constant $k = f o r c e / l e n g t h .$

$[M^{0} L^{0} T^{- 1}] = [M^{x} {({MT}^{- 2})}^{y}] = [M^{x + y} T^{- 2 y}]$

$\Rightarrow$ $x + y = 0, - 2 y = - 1$ or $y = \frac{1}{2}$

Therefore, $x = - \frac{1}{2}$

Stream:NTA_ABHYASSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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